Ivanir was born in Chernovtsi (now Chernivtsi), Ukrainian SSR, on September 6, 1968. His family emigrated to Israel in 1972. His father, Alexander "Sasha", was an English Teacher, and his mother, Malka, a German Teacher. His maternal grandfather, Meshulem Surkis, was a Yiddish Writer, Journalist, actor, and theatre critic, who was a well known Activist in the Yiddish cultural world.
His first major film role was in Steven Spielberg's 1993 Oscar-winning epic Schindler's List. He rejoined with Spielberg twice thereafter, first for a cameo appearance in The Terminal, then again for The Adventures of Tintin: The Secret of the Unicorn. Mark held a pivotal role in Robert De Niro's 2006 film, The Good Shepherd, for which he won the Silver Bear Award at the Berlin Film Festival, later landing a role in Barry Levinson's What Just Happened, this time acting alongside De Niro.
In 2011, he appeared in Universal's Johnny English Reborn, Universal's Big Miracle and 360.
His biggest part to date was on the critically acclaimed A Late Quartet, released from RKO pictures in the United States, in fall 2012. The film was voted as one of the New York Daily News 10 top films of the year. Ivanir plays Daniel Lerner, the first violin of the string quartet, whose other members are played by Philip Seymour Hoffman, Catherine Keener and Christopher Walken.
In 2016 Ivanir had a recurring role on Homeland as Russian intelligence agent Ivan Krupin. The season was nominated for the SAG Awards and for the Emmy’s.
In 2018, he co-starred in the film Entebbe, directed by the creator of Narcos, José Padilha, and Bill Hader's HBO comedy Barry, in which he recurs as three Chechen brothers. He will appear in The Red Sea Diving Resort, as the head of the Mossad, alongside Sir Ben Kingsley, Chris Evans and Greg Kinnear.
